[thedoc (OP)]

Chris Grieshaber asked the Naked Scientists:
   
If I run at 10km per hour inside a plane traveling at 800km an hour what speed am I moving at?


What do you think?

[evan_au]

In Physics, you always need to measure speed relative to some "Frame of Reference".

There is no "Perfect" frame of reference, so all of the following answers are equally correct:

• as seen by someone standing on the ground, you are traveling at 810 kph across the sky.
  
• as seen by to someone sitting on the plane, you are traveling at 10 kph down the aisle.
  
• as seen by the mobile phone in your pocket, you are effectively stationary.
  
• as seen by someone standing on Pluto, you are traveling at 100000 kph around the Sun.

The idea that there is no "right" answer was a bit of a shock to some people when Einstein introduced his theory of relativity.

[Bill S]

Of course, one should use the relativistic velocity addition formula to answer your question, but at the low speeds (compared to the speed of light) you mention, the difference would be negligible.

[CliffordK]

Can I just say that 800 kph has one significant figure....  (although it is one of those ambiguous numbers).

So, you're still traveling 800 kph  []

[jeffreyH]

It all depends upon the forces acting on the plane. In a severely time dilated field both the runner and the plane would appear to be traveling faster than would be apparent to a distant observer. Simply because while the object has a specific velocity as viewed remotely time for the passengers has slowed so the relationship between perceived distance traveled over time taken has changed.

[syhprum]

Speed is of course a vector quantity but due to the geometry of the aircraft your speed can only add or subtract from the speed of the aircraft relative to the ground excluding SR.
If you were in a large saucer shaped alien UFO and could run in any direction the angle relative to the craft would have to be taken into account.
Warning do not try this on a Ryanair trip !

[alancalverd]

810 kph if you are running towards the nose, 790 kph if you are running towards the tail.

Now some smartarse is bound to ask "relative to what?" and the answer is "the air around the plane", because that is what planes fly through. Unless the nominal "800 kph" is ground speed measured by a GPS system, of course.

[syhprum]

I don't think many normal commercial flights go as fast as 800 kph I have a theory that pilots go as slow as they dare to gain brownie points by saving fuel

[chris]

In our "Science of Star Wars" programme we looked at the issue of relativity and covered this issue - albeit by firing a ball from a moving trolley to prove the point - in this feature about relativity and high-speed travel.

[yor_on]

If you're running back and forth inside that plane I guess you could see it as being still :)
In that case it's 800 km/h

[Bored chemist]

From the point of view of an ant on your head, you are not moving at all.

[Bill S]

Now some smartarse is bound to ask "relative to what?" and the answer is "the air around the plane"

Naturally the smartarse is bound to ask: "What about wind speed/direction?" and we all know where it goes from there!

Did someone say: "to hell in a handcart"?

[alancalverd]

Gotchas!

The rated cruising speed of most jet airliners is 780 - 850 kph depending on type and altitude, but generally in the range Mach  0.75 - 0.9.

No, pilots do not fly slower to save fuel. Jet aircraft are most efficient at their rated cruise Mach number for a given weight and altitude. If you slow down below your filed flight plan speed you may lose your approach slot, with all sorts of expensive and inconvenient consequences, and end up burning more fuel anyway..

Wind speed is irrelevant to airspeed - the plane flies at its TAS through ambient air, regardless of where the ambient air is going, or how fast.

[Bill S]

Wind speed is irrelevant to airspeed - the plane flies at its TAS through ambient air, regardless of where the ambient air is going, or how fast.

When did mundane facts prevent the crackpots from speculating?